Graduate PD code yields two different knot diagrams

[sophiatev]

TL;DR

The same PD code seems to yield two different knot diagrams of the Hopf link

The PD code [(2, 3, 1, 4), (4, 1, 3, 2)] seems to map to a non-unique knot diagram. I can describe the following two Hopf links with different orientations with this same PD code. As I understand it, while a link diagram does not have a unique PD code, a given PD code should map to just one knot diagram. Am I missing something?

 

[jedishrfu]

Are these supposed to be knots? Both diagrams look like two interconnected rings not knots. Perhaps that's why things aren't working.

Here's a trefoil knot that looks similar to yours but has an extra loop:

https://en.wikipedia.org/wiki/Trefoil_knot

and here's a table of many knots:

http://katlas.org/wiki/The_Rolfsen_Knot_Table

 

[sophiatev]

Sorry, the PD code maps to a unique *link* diagram, so the Hopf link is a valid diagram (also, a ring is the unknot so it's still a knot, right? The Hopf link is just two linked unknots)

 

[Maarten Havinga]

I don't know if it helps, but:

Make half a turn (the least complicated direction) of one of the 4 rings around the horizontal axis.